Averaging generalized scalar-field cosmologies III: Kantowski–Sachs and closed Friedmann–Lemaître–Robertson–Walker models

Abstract

Scalar-field cosmologies with a generalized harmonic potential and matter with energy density $$\rho _m$$ ρ m , pressure $$p_m$$ p m , and barotropic equation of state (EoS) $$p_m=(\gamma -1)\rho _m, \; \gamma \in [0,2]$$ p m = ( γ - 1 ) ρ m , γ ∈ [ 0 , 2 ] in Kantowski–Sachs (KS) and closed Friedmann–Lemaître–Robertson–Walker (FLRW) metrics are investigated. We use methods from non-linear dynamical systems theory and averaging theory considering a time-dependent perturbation function D. We define a regular dynamical system over a compact phase space, obtaining global results. That is, for KS metric the global late-time attractors of full and time-averaged systems are two anisotropic contracting solutions, which are non-flat locally rotationally symmetric (LRS) Kasner and Taub (flat LRS Kasner) for $$0\le \gamma \le 2$$ 0 ≤ γ ≤ 2 , and flat FLRW matter-dominated universe if $$0\le \gamma \le \frac{2}{3}$$ 0 ≤ γ ≤ 2 3 . For closed FLRW metric late-time attractors of full and averaged systems are a flat matter-dominated FLRW universe for $$0\le \gamma \le \frac{2}{3}$$ 0 ≤ γ ≤ 2 3 as in KS and Einstein–de Sitter solution for $$0\le \gamma <1$$ 0 ≤ γ < 1 . Therefore, a time-averaged system determines future asymptotics of the full system. Also, oscillations entering the system through Klein–Gordon (KG) equation can be controlled and smoothed out when D goes monotonically to zero, and incidentally for the whole D-range for KS and closed FLRW (if $$0\le \gamma < 1$$ 0 ≤ γ < 1 ) too. However, for $$\gamma \ge 1$$ γ ≥ 1 closed FLRW solutions of the full system depart from the solutions of the averaged system as D is large. Our results are supported by numerical simulations.

Time-averaging axion-like interacting scalar fields models

“…This procedure is supported by numerical simulations (see related work [150]). Similar arguments can be provided using the tools of [143] or, as is the case in this research, by implementing an analogous program as in the references [147][148][149] but for averaging multi-scalar fields cosmologies.…”

“…Perturbations methods and averaging methods were used, for example, in [142][143][144][145][146][147][148][149][150]. One idea is to construct a timeaveraged version of the original system, solving it; the oscillations of the original system are smoothed out [150].…”

“…In the Refs. [147][148][149] a research program "Averaging generalized scalar field cosmologies" was started. It consisted of using asymptotic methods and averaging theory [158] to explore the solution's space of scalar field cosmologies with generalized harmonic potential in vacuum or minimally coupled to matter.…”

“…It consisted of using asymptotic methods and averaging theory [158] to explore the solution's space of scalar field cosmologies with generalized harmonic potential in vacuum or minimally coupled to matter. As a difference with [147,148], where the Hubble parameter was used as a timedependent perturbation parameter, in [149] systems where Hubble scalar is not monotonic were studied.…”

“…In this paper we generalize the program initiated in [147][148][149] to two-fluid cosmological models. To this goal, we analyze an axion-like coupled scalar fields model following Ref.…”